Turn the wheel of a Tesla Model Y and your hands mostly steer a sensor. A torsion-bar torque sensor on the pinion measures your effort, an ECU decides how much help you get, and a motor slung under the rack delivers it — through a 42:16 toothed belt and a ball-screw nut that recirculates a train of steel balls to push the rack sideways with almost no friction. The mechanical path — column, double-Cardan universal joints, pinion — never goes away; it is the backbone the electric assist rides on.
The bench carries the Model Y’s real front-axle numbers: 2.00 turns lock-to-lock, a 2,890 mm wheelbase on a 1,636 mm track, and a curb turning circle just under twelve metres. Steering geometry does the rest: tie rods on a rear-mounted rack steer each knuckle about a virtual kingpin axis set by an upper control arm and two separate lower links, and Ackermann behaviour — the inner wheel turning tighter than the outer — falls out of the linkage on its own, plotted live in the plan-view inset.
Nothing here is keyframed. A deterministic one-degree-of-freedom kernel solves the whole chain — exact Cardan vector kinematics, the ball-screw lead constraint, the tie-rod sphere intersection — and twelve invariants are machine-checked every time the exhibit boots, from double-Cardan cancellation to tie-rod length conservation. It is the same lesson DigiSim teaches with logic gates: build the constraints honestly and the behaviour emerges.
Specifications
- Architecture
- Belt-drive rack EPS — 42:16 synchronous belt, 10 mm-lead ball screw
- Alignment
- Model Y spec: 2.00 turns lock-to-lock, ≈10.6:1 overall, ≈11.9 m circle
- Geometry
- 2,890 mm wheelbase · 1,636 mm track · lock angles 37.9°/29.7°
- Simulated
- Exact Cardan kinematics, emergent Ackermann, 12 boot invariants
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